Statistical Density Estimation Using Threshold Dynamics for Geometric Motion

Authors:
Tijana Kostić;Andrea Bertozzi
Affiliations:
Mathematics Department, UCLA, Los Angeles, USA 90095-1555;Mathematics Department, UCLA, Los Angeles, USA 90095-1555
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

Our goal is to estimate a probability density based on discrete point data via segmentation techniques. Since point data may represent certain activities, such as crime, our method can be successfully used for detecting regions of high activity. In this work we design a binary segmentation version of the well-known Maximum Penalized Likelihood Estimation (MPLE) model, as well as a minimization algorithm based on thresholding dynamics originally proposed by Merriman et al. (The Computational Crystal Growers, pp. 73---83, 1992). We also present some computational examples, including one with actual residential burglary data from the San Fernando Valley.